Two categories are equivalent when they are isomorphic up to an isomorphism
Thaaaaat is a confusing sentence. But thankfully, the rest of your comment clears things up. Why do you want this notion of equivalence or adjunction, rather than the stricter notion of isomorphism of categories?
Thaaaaat is a confusing sentence. But thankfully, the rest of your comment clears things up.
Why do you want this notion of equivalence or adjunction, rather than the stricter notion of isomorphism of categories?